Mixture Question

Question

A coffee distributor needs to mix a(n) Rift Valley coffee blend that normally sells for $10.20 per pound with a Organic Free Trade coffee blend that normally sells for $11.50 per pound to create 80 pounds of a coffee that can sell for $10.83 per pound. How many pounds of each kind of coffee should they mix?

Answer 1

Let x represent rift valley coffee and y represent organic free trade coffee.

Since the problem states that these two coffee blends are to be mixed to create 80 pounds of coffee, then we arrive at the following:

   quantity of Rift Valley coffee blend + quantity of Organic Free Trade coffee blend = 80

OR    x + y = 80

and 2nd equation will be 10.20x + 11.50y = 10.83(80)

Simplify the equation to get the value of x and y.

So from 1st equation let's say x = 80-y substitute this in 2nd equation

10.20(80-y) + 11.50y = 866.4 --> 816 - 10.20y + 11.50y = 866.4

1.3y = 50.4 --> y = 38.76 ≈ 39

now keep value of y in 1st equation x = 80- 39 = 41

Solution:  x = 41  and  y = 39

Thus, they must mix 41 pounds of the Rift Valley coffee blend and 39 pounds of the Organic Free Trade coffee blend .